This is a demonstration of color anamorphosis in its simpler form: with regard to value only. In order to mimic the original cube, the faces of the anamorphic drawing must be painted in such a way that the product (n.u)I is preserved, where n is the normal to the surface, u is the unit vector of the light direction (assumed at infinity) and I is the intensity of the light source. Obviously this can't always be done. Unlike conical anamorphosis, color anamorphosis doesn't always have a solution.
Above: some playful arrangement of a cube and its plane anamorph. Notice how color matching is wholly dependent on the original configuration with regard to light source type and position.
Equirectangular spherical perspective isn't as nice as azimuthal equidistant spherical perspective in terms of great circle plots. Great circles plot like longitude=arctan(a.cos(latitude)), which with the apex at high latitudes makes for some rather squarish lines. But these too can be well approximated by ruler and compass. see my upcoming paper "Guidelines for drawing VR panoramas in equirectangular perspective".
The good thing about these equirectangular perspectives is that Flickr, Google, Facebook, and so on, know how to render them as VR panoramas, which basically means, as interactive planar anamorphoses. So: Click on the picture below to see it as a VR panorama.
Equirectangular perspective of three pencils of straight lines, going to 15, 45, and 75 longitude vanishing points respectively, from left to eight. We can see that these lines take a rather complex sigmoidal shape.
Click on the picture below to see it as a VR panorama.
